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Netlab Reference Manual scg
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<H1> scg
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<h2>
Purpose
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Scaled conjugate gradient optimization.

<p><h2>
Description
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<CODE>[x, options] = scg(f, x, options, gradf)</CODE> uses a scaled conjugate 
gradients
algorithm to find a local minimum of the function <CODE>f(x)</CODE> whose
gradient is given by <CODE>gradf(x)</CODE>.  Here <CODE>x</CODE> is a row vector
and <CODE>f</CODE> returns a scalar value.
The point at which <CODE>f</CODE> has a local minimum
is returned as <CODE>x</CODE>.  The function value at that point is returned
in <CODE>options(8)</CODE>.

<p><CODE>[x, options, flog, pointlog, scalelog] = scg(f, x, options, gradf)</CODE>
also returns (optionally) a log of the function values
after each cycle in <CODE>flog</CODE>, a log
of the points visited in <CODE>pointlog</CODE>, and a log of the scale values
in the algorithm in <CODE>scalelog</CODE>.

<p><CODE>scg(f, x, options, gradf, p1, p2, ...)</CODE> allows
additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. 
  
The optional parameters have the following interpretations.

<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error 
values in the return argument <CODE>errlog</CODE>, and the points visited
in the return argument <CODE>pointslog</CODE>.  If <CODE>options(1)</CODE> is set to 0,
then only warning messages are displayed.  If <CODE>options(1)</CODE> is -1,
then nothing is displayed.

<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
of <CODE>x</CODE> at the solution.  If the absolute difference between
the values of <CODE>x</CODE> between two successive steps is less than
<CODE>options(2)</CODE>, then this condition is satisfied.

<p><CODE>options(3)</CODE> is a measure of the precision required of the objective
function at the solution.  If the absolute difference between the
objective function values between two successive steps is less than
<CODE>options(3)</CODE>, then this condition is satisfied.
Both this and the previous condition must be
satisfied for termination.

<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function.

<p><CODE>options(10)</CODE> returns the total number of function evaluations (including
those in any line searches).

<p><CODE>options(11)</CODE> returns the total number of gradient evaluations.

<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.

<p><h2>
Examples
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An example of 
the use of the additional arguments is the minimization of an error
function for a neural network:
<PRE>

w = scg('neterr', w, options, 'netgrad', net, x, t);
</PRE>


<p><h2>
Algorithm
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The search direction is re-started after every <CODE>nparams</CODE> 
successful weight updates where <CODE>nparams</CODE> is the total number of 
parameters in <CODE>x</CODE>. The algorithm is based on that given by Williams
(1991), with a simplified procedure for updating <CODE>lambda</CODE> when
<CODE>rho < 0.25</CODE>.

<p><h2>
See Also
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<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr>
<b>Pages:</b>
<a href="index.htm">Index</a>
<hr>
<p>Copyright (c) Ian T Nabney (1996-9)


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